Write the relation between beta function and gamma function.

The relation between the beta function and the gamma function can be expressed as follows:

1. Start with the definition of the beta function: The beta function, denoted as B(x, y), is defined as: B(x, y) = ∫[0, 1] t^(x-1) * (1-t)^(y-1) dt

2. Next, consider the gamma function: The gamma function, denoted as Γ(z), is defined as: Γ(z) = ∫[0, ∞] t^(z-1) * e^(-t) dt

3. Now, we can establish the relation between the beta function and the gamma function: B(x, y) = Γ(x) * Γ(y) / Γ(x + y)

   This relation can be derived by using the properties of the gamma function and performing some algebraic manipulations.

   It is important to note that the relation between the beta function and the gamma function is useful in various mathematical and statistical applications, such as in the calculation of probabilities and in solving integral equations.